Question

If in a wire of Young�s modulus $Y$ , longitudinal strain $X$ is produced then the potential energy stored in its unit volume will be

• A. $0.5 \,Y \,X ^2$
• B. $0.5 \,Y^2 X$
• C. $2\,Y\,X^2$
• D. $Y\,X^2$

Answer 1

Answer: (A)

$0.5 \,Y \,X ^2$

Answer 2

Elastic potential energy per unit volume
$U=\frac{1}{2}\times \text{stress}\times \text{strain}$
From definition of Young's modulus of wire
$Y=\frac{\text{stress}}{\text{strain}}$
$\Rightarrow$ Stress $=Y\times$ strain
Given, strain=X
= $U=\frac{1}{2}TX^2$
$\Rightarrow U=0.5YX^2$